Let X; be independent Uniform(-9,9) random variables, fori=1,2, ..., 14. Let Y = X1+X2+...+X14 - (b) Find which of the following statements are correct for the moment generating function (mgf) My(t) of Y. I It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 I It is equal to 9 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14 I It is equal to the sum of the mgfs of the Xi, for i=1,...,14 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to the product of the mgfs of the Xi, for i=1...14

Let X; be independent Uniform(-9,9) random variables, fori=1,2, ..., 14. Let Y = X1+X2+...+X14 - (b) Find which of the following statements are correct for the moment generating function (mgf) My(t) of Y. I It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14 It is equal to the mgf of any Xi to the power of 1/14, for i=1,...,14 I It is equal to 9 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14 I It is equal to the sum of the mgfs of the Xi, for i=1,...,14 The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t. It is equal to the product of the mgfs of the Xi, for i=1...14

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

part a) Which values of the constants A, B, C, D are correct

part b) Find which of the following statements are correct

part c) Find the expected value and variance of Y

Let X; be independent Uniform(-9,9) random variables, for i=1, 2, .., 14.
Let Y = X,+X2+...+X14 .
(b) Find which of the following statements are correct for the moment generating function (mgf) My(t) of Y.
It is equal to 14 times the mgf of Xi, for some integer i between 1 and 14
I It is equal to the mgf of any Xi to the power of 1/14, for i=1,.,14
It is equal to 9 times the mgf of any Xi to the power of 14, for some integer i between 1 and 14
It is equal to the sum of the mgfs of the Xi, for i=1,.,14
The mgf of 2Y is obtained by replacing in the mgf of Y the value t by 2t.
I It is equal to the product of the mgfs of the Xi, for i=1,..,14

Let X be a Uniform(-9,9) random variable.
(a) The moment generating function of X is Mx(t) = A(eBr – ec) tº, for some tin the neighbourhood of zero.
Which values of the constants A, B, C, D are correct (following the same order as they occur here)?
0.22, 9, -9, -1
4.50, 9, -9, -1
4.50, -9, 9, -1
0.22 9, -9, 1
0.06, 9, -9, -1
0.06, -9, 9, 1

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